Margin of error and sample size in a poll

A poll reports the share of people who hold a view, such as 48 percent support for a proposal. That figure comes from the people who answered, not from the whole population. The margin of error is the range around the reported share that reflects how much the result could differ from the true figure if the pollster had questioned a different random group of the same size. A margin of 3 percentage points means the true share is likely within 3 points above or below the reported number, using the 95 percent confidence level that most public polls report.

Reading that range correctly matters most when two numbers are close. A lead of 2 points in a poll with a margin of 3 points does not show that one side is ahead. It shows that the poll cannot tell the two sides apart with confidence. Many news reports skip this step and describe the leader as winning, when the honest summary is that the race looks close.

What the margin of error measures

The margin of error captures sampling variation, the normal difference you would expect between two random samples drawn from the same population. Each sample includes some people and leaves out others, so its result shifts a little. Statisticians can calculate how large those shifts typically are. At the 95 percent level, the margin of error is about 1.96 times the standard error of the reported share.

For a share near 50 percent in a simple random sample, the margin of error at 95 percent confidence is close to 1 divided by the square root of the sample size, expressed in percentage points. That shortcut is accurate enough for reading polls. A sample of 1,000 people gives a margin of about 3 points. A sample of 400 gives about 5 points.

The margin of error does not cover everything that can go wrong. It says nothing about question wording, people who declined to answer, or whether the sample represents the population the report describes. Those errors can be larger than sampling variation, and they are not included in the printed range.

How sample size changes the range

Because the margin depends on the square root of the sample size, gains in precision slow down as the sample grows. Doubling the number of respondents shrinks the margin by roughly 30 percent, not by half. To cut the margin in half, a pollster needs four times as many people. A poll of 100 respondents carries a margin near 10 points, too wide to say much about a race separated by a few points. A poll of 2,500 has a margin near 2 points.

The same logic applies to subgroups. A poll of 1,000 adults might break out results for young adults, a group of 150 respondents. For that subgroup, the margin is near 8 points, far wider than the headline figure. Breakdowns by age, region or party often rest on small numbers, so a difference of 10 points between two such groups may not be meaningful. When a report gives a subgroup result, check how many people it is based on.

Why a gap between two candidates needs a larger margin

The margin of error on one share is not the right yardstick for a lead. A lead is the difference between two shares, and both shares come from the same sample, so their errors are linked. For two candidates who are close together, the margin on the gap is often close to twice the margin on either candidate's share. In a poll of 1,000 people showing 48 percent for one candidate and 46 percent for the other, each share has a margin near 3 points, but the 2-point lead has a margin near 6 points.

That is why the phrase "within the margin of error" appears so often in coverage. The accurate meaning is that the poll cannot say which candidate is ahead, even though the reported numbers point one way. If a report gives only one margin of error, assume the margin on a lead is roughly double that figure. A lead larger than that range is stronger evidence, though it is still a single poll and should be read alongside other polls.

Who answered matters as much as how many

The margin of error assumes a random sample, in which every member of the population had a known chance of being selected. Many polls rely on online panels or other methods where people opt in, and pollsters often adjust results through weighting. Weighting gives some respondents more influence so the sample resembles the population on factors such as age, sex, education and region. Weighting can reduce bias, but it cannot correct for a group that differs in ways the weights do not measure.

When you read a poll, look for the population described. Adults, registered voters and likely voters can produce different results on the same questions. Check the dates the poll was in the field, because opinion can move between interviews and publication. A thorough poll report usually states the sample size, the population, how respondents were contacted, the dates, the margin of error and whether the results were weighted. If those details are missing, the margin in the headline may understate the true uncertainty.

A simple routine helps. Find the sample size, the population and the margin of error. Estimate the margin on the lead, which is roughly double the stated figure when the candidates are close. Then ask whether the gap clearly exceeds that range. If it does not, describe the race as close rather than as a lead, and look for other polls before drawing a firmer conclusion.